Periodic orbits of a chaotic system are a rich source of qualitative information about the dynamical system. For example, the presence of unstable periodic orbits on the attractor is a typical characteristic of a chaotic system. The abundance of unstable periodic orbits have been utilized in a wide variety of theoretical and practical applications for analyzing, compressing, and processing signals. Therefore, it is desirable to be able to provide new and improved systems and methods for analyzing signals using orbits of chaotic systems.